Multifractal eigenfunctions for a singular quantum billiard

Autor: Henrik Ueberschär, Jon P Keating

Publikováno v: Communications in Mathematical Physics
Communications in Mathematical Physics, Springer Verlag, 2021, ⟨10.1007/s00220-021-04214-8⟩

Whereas much work in the mathematical literature on quantum chaos has focused on phenomena such as quantum ergodicity and scarring, relatively little is known at the rigorous level about the existence of eigenfunctions whose morphology is more comple

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0ca545b32f48e3ee6d0dab9dd8d2ebd2
http://arxiv.org/abs/2103.13448

Symmetric Function Theory and Unitary Invariant Ensembles

Autor: Bhargavi Jonnadula, Jon P Keating, Francesco Mezzadri

Publikováno v: Jonnadula, B, Keating, J & Mezzadri, F 2021, ' Symmetric function theory and unitary invariant ensembles ', Journal of Mathematical Physics, vol. 62, no. 9, 093512 . https://doi.org/10.1063/5.0048364

Representation theory and the theory of symmetric functions have played a central role in Random Matrix Theory in the computation of quantities such as joint moments of traces and joint moments of characteristic polynomials of matrices drawn from the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7a15ccb684094ee5cfa8e76b65a0d205
http://arxiv.org/abs/2003.02620

Sums of divisor functions in $$\mathbb {F}_q[t]$$ F q [ t ] and matrix integrals

Autor: Brad Rodgers, Edva Roditty-Gershon, Zeév Rudnick, Jon P Keating

Publikováno v: Mathematische Zeitschrift. 288:167-198

We study the mean square of sums of the kth divisor function $$d_k(n)$$ over short intervals and arithmetic progressions for the rational function field over a finite field of q elements. In the limit as $$q\rightarrow \infty $$ we establish a relati

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::2adbfdb7919ff0536584fc7a162b79f9
https://doi.org/10.1007/s00209-017-1884-1

Arithmetic correlations over large finite fields

Autor: Edva Roditty-Gershon, Jon P Keating

Publikováno v: Keating, J P & Roditty-Gershon, E 2016, ' Arithmetic Correlations Over Large Finite Fields ', International Mathematics Research Notices, vol. 2016, no. 3, pp. 860-874 . https://doi.org/10.1093/imrn/rnv157

The auto-correlations of arithmetic functions, such as the von Mangoldt function, the M\"obius function and the divisor function, are the subject of classical problems in analytic number theory. The function field analogues of these problems have rec

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ebfde34e26ae0c195f02be0a1936bb5d
https://ora.ox.ac.uk/objects/uuid:a1e54831-1864-4b8d-beb1-1229c11105c0

Pair correlation and twin primes revisited

Autor: Jon P Keating, Brian Conrey

Publikováno v: Proceedings. Mathematical, Physical, and Engineering Sciences
Conrey, B & Keating, J P 2016, ' Pair correlation and twin primes revisited ', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 472, no. 2194, 20160548 . https://doi.org/10.1098/rspa.2016.0548

We establish a connection between the conjectural two-over-two ratios formula for the Riemann zeta-function and a conjecture concerning correlations of a certain arithmetic function. Specifically, we prove that the ratios conjecture and the arithmeti

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cf02100adae21c71dced5a02bfd7d218
https://doi.org/10.1098/rspa.2016.0548